Find K Pairs with Smallest Sums

You are given two integer arrays nums1 and nums2 sorted in ascending order and an integer k.

Define a pair (u,v) which consists of one element from the first array and one element from the second array.

Find the k pairs (u1,v1),(u2,v2) ...(uk,vk) with the smallest sums.

Example 1:

Given nums1 = [1,7,11], nums2 = [2,4,6],  k = 3

Return: [1,2],[1,4],[1,6]

The first 3 pairs are returned from the sequence:
[1,2],[1,4],[1,6],[7,2],[7,4],[11,2],[7,6],[11,4],[11,6]

Example 2:

Given nums1 = [1,1,2], nums2 = [1,2,3],  k = 2

Return: [1,1],[1,1]

The first 2 pairs are returned from the sequence:
[1,1],[1,1],[1,2],[2,1],[1,2],[2,2],[1,3],[1,3],[2,3]

Example 3:

Given nums1 = [1,2], nums2 = [3],  k = 3 

Return: [1,3],[2,3]

All possible pairs are returned from the sequence:
[1,3],[2,3]

Tips:

• 和Kth Smallest Element in a Sorted Matrix几乎一样，唯一的区别就是这题给了两个array而那题给了一个矩阵。

• 想象一下，把这题的两个数组变成num1.length * num2.length的矩阵，例如将exp1变为

    matrix = 
       [ 1*2, 1*4 , 1*6 ],
       [ 7*2, 7*4 , 7*6 ],
       [11*2, 11*4, 11*6]
  

• 与那题一样，先将第一行加入heap，然后取heap里的最小值，加入矩阵中这个最小值下面的数，并在result里添加当前最小值。（注意添加的是值不是坐标哟）

• 仍然要注意的是要新建一个node类，并重写compareTo方法，不然无法获取这个点的坐标。注意在重写compareTo那里一定要public，不然会出错！

Code:

public class Solution {
    public List<int[]> kSmallestPairs(int[] nums1, int[] nums2, int k) {
        List<int[]> result = new ArrayList<>();
        PriorityQueue<Node> heap = new PriorityQueue<>();
        if (nums1 == null || nums1.length == 0 || nums2 == null || nums2.length == 0 || k <= 0) {
            return result;
        }
        for (int i = 0; i < nums2.length; i++) {
            heap.add(new Node(0, i, nums1[0] + nums2[i]));
        }
        for (int i = 0; i < Math.min(k, nums1.length * nums2.length); i++) {
            Node curt = heap.remove();
            int[] temp = {nums1[curt.x], nums2[curt.y]};
            result.add(temp);
            if (curt.x == nums1.length - 1) {
                continue;
            }
            heap.add(new Node(curt.x + 1, curt.y, nums1[curt.x + 1] + nums2[curt.y]));
        }
        return result;
    }
    class Node implements Comparable<Node>{
        int x;
        int y;
        int val;
        public Node(int x, int y, int val) {
            this.x = x;
            this.y = y;
            this.val = val;
        }
        public int compareTo(Node that) {
            return this.val - that.val;
        }
    }
}